Methods and devices for determining optimal agent dosages

ABSTRACT

The present invention is generally directed to methods and devices for determining dosing for a medical agent. In some embodiments, a mathematical algorithm is employed for computing erythropoiesis-stimulating agents dosing for treating anemia in a subject, e.g., a human subject. Any suitable dosing may be used, e.g., intravenous, subcutaneous, or oral dosing. In some cases, dosing for a wide range of subject types and health conditions can be achieved using the devices and methods disclosed herein.

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 61/701,527, filed Sep. 14, 2012, by Chait, et al.,incorporated herein by reference.

FIELD

The present invention, in some embodiments thereof, relates to methodsand devices for effectively determining an optimal dosage program for amedical agent. The instant invention, in some embodiments, allows forsuch determinations with algorithms that applicable to subjects from awide range of ages and racial backgrounds.

BACKGROUND

Blood is critical for human health. Red blood cells move carbon dioxideout of and oxygen into metabolizing cells throughout the body. The keycomponent for this action is the protein hemoglobin. Hemoglobin, atetrameric iron protein, is produced according to the biological needsof the body and moves throughout the body in red blood cells. In somecases, the body is unable to produce enough red blood cells, e.g., dueto some form of illness that may include renal failure. Such conditionscan be extremely dangerous, as the brain in particular has a high oxygendemand.

Erythropoietin (EPO) is a critical material in the production of redblood cells. EPO is produced in the renal cortex. EPO was also one ofthe first recombinant drugs to receive FDA approval and find wide use.However, methods and devices for effectively delivering EPO to a needypatient are critical. Optimization of EPO and similar drug delivery canenhance the quality of life for those who cannot produce EPO on theirown, and efficient dosing of EPO can save enormous amounts of money fora health provider such as an HMO or hospital.

The prior art generally describes delivery of EPO to anemic patients ina manner that is case-specific and requires frequent dosing. However,many current anemia management protocols (or AMPs) fail to stabilizehemoglobin concentrations in a subject, which may lead to adversemedical complications or even death of the subject. Accordingly,improvements in such delivery and control are needed.

SUMMARY

The present invention, in some embodiments thereof, relates to methodsand devices for effectively determining an optimal dosage program for amedical agent. The subject matter of the present invention involves, insome cases, interrelated products, alternative solutions to a particularproblem, and/or a plurality of different uses of one or more systemsand/or articles.

One aspect of the present invention is generally directed to methods fordetermining optimal dosing of erythropoiesis agents for an anemicsubject.

In another aspect, the present invention is generally directed to amethod for computing erythropoiesis-stimulating agents (ESAs) dosing(e.g., intravenously, subcutaneously, orally, etc.), for treating anemiain a subject, such as a human subject. In some cases, the methodincludes acts of measuring a value of at least one biochemical propertyrelated to an anemia status in the subject; determining a differencebetween the value of the at least one biochemical property and apredetermined optimal value for the property; and, employing a computingelement with a mathematical algorithm to calculate a required ESA dosagebased on the difference. In some cases, the algorithm may maintainpredetermined target performance criteria for a range of biochemicalproperty values in a plurality of predetermined physiological factorsaffecting the value of the at least one biochemical property.

In one set of embodiments, the biochemical property is hemoglobinconcentration.

In another set of embodiments, the range of target values is 8 g/dl and14 g/dl

In another set of embodiments, the dosing involves administration ofrecombinant human erythropoietin (rHuEPO).

In another set of embodiments, the rHuEPO is produced in a non-humansource using synthetically or biologic methods.

In another set of embodiments, the dosing involves administration ofnovel erythropoiesis stimulating protein (NESP).

In another set of embodiments, the dosing involves administration of HIFstabilizing agent.

In another set of embodiments, the value is determined 3 times a week,once a week, bi-weekly, monthly, or other intervals.

In another set of embodiments, the anemia is associated with renalfailure.

In another set of embodiments, the physiological factors include redblood cell lifespan, production rate of new red blood cells, and ironstatus.

In another set of embodiments, the physiological factors includeintravenous, subcutaneous, or oral delivery of iron to the subject.

The present invention additionally includes, in another aspect, a methodfor applying an anemia management protocol (AMP) for treating anemia ina subject, such as a human subject. For example, in certain methods, themethod includes acts of measuring a value of at least one biochemicalproperty related to an anemia status in the subject; determining adifference between the value of the at least one biochemical propertyand a predetermined value for the property; and, employing a computingelement with a mathematical algorithm to calculate a required dosage forerythropoiesis-stimulating agents (ESA) based on the difference. In somecases, the algorithm may include a step for reducing the sensitivity ofthe anemia management protocol to variability in the subject'sresponsiveness to the erythropoiesis-stimulating agents.

In one set of embodiments, the algorithm includes a step to reduce thesensitivity of the AMP to variations in concentrations of iron andvitamins in the subject's blood.

In another set of embodiments, the algorithm includes a step forreducing the sensitivity of the AMP to variability in the value of thebiochemical property.

In another set of embodiments, the algorithm includes a step foradjusting the gain of the AMP for a present level of the subject'sresponsiveness to the ESA.

In another set of embodiments, the algorithm includes a step forcalculating dosage for the ESA for the subject over a predetermineddosing schedule.

In another set of embodiments, the predetermined dosing schedule isselected from the following: daily, three times per week, weekly,bi-weekly, and monthly.

In another set of embodiments, the step includes an integrator or anapproximated discrete-time integrator.

In another set of embodiments, the AMP remains fixed for any targetvalues of the property in the range 8 g/dl and 14 g/dl

In another set of embodiments, the integrator is described by theequation:

$\frac{z}{z - 1},$

and the approximated discrete-time integrator is described by:

$\frac{z}{z - a},$

wherein the value of a is near 1.

In another set of embodiments, the discrete-time integrator is selectedfrom the following: Forward Euler, Backward Euler, Trapezoidal method,second-order accurate method, or third order accurate method.

In another set of embodiments, the algorithm includes at least one stepfor reducing the sensitivity of the AMP to variability in the value ofthe measured biochemical property.

In another set of embodiments, the algorithm includes an estimator forthe subject's responsiveness to ESAs.

In another set of embodiments, the estimator of the property isdescribed by the following equation:

${{estimated}\mspace{14mu} {responsivenss}} = {\frac{{mean}\left( {{weekly}\mspace{14mu} {Hgb}\mspace{14mu} {measurements}\mspace{14mu} {during}\mspace{14mu} {past}\mspace{14mu} n\mspace{14mu} {weeks}} \right)}{{mean}\left( {{weekly}\mspace{14mu} {ESA}\mspace{14mu} {doses}\mspace{14mu} {during}\mspace{14mu} {past}\mspace{14mu} n\mspace{14mu} {weeks}} \right)}.}$

In another set of embodiments, the gain associated with the AMP isadjustable in an inversely proportional manner to the responsiveness.

The present invention, in yet another aspect, is generally directed to adevice for delivering erythropoiesis-stimulating agents (ESA) to asubject, such as a human subject. In some cases, theerythropoiesis-stimulating agents may be an optimized amount. Theerythropoiesis-stimulating agents may be delivered by any suitabletechnique, for example, intravenously, subcutaneously, orally, etc. Insome cases, the erythropoiesis-stimulating agents may be delivered bythe device for treating anemia in the subject,

In one set of embodiments, the device includes one or more of ameasuring element adapted to measure a value of at least one biochemicalproperty related to an anemia status in the subject; a communicationelement adapted to communicate the value to a computing element; acomputing element adapted to calculate a difference between the value ofthe at least one biochemical property and a predetermined value or rangeof values for the property, the element adapted to employ a mathematicalalgorithm to calculate a required ESA dosage based on the difference. Insome cases, the algorithm may remain fixed for any target values of theproperty in the range 8 g/dl and 14 g/dl and, a delivery element fordelivering the ESA to the subject.

In another set of embodiments, the erythropoiesis-stimulating agentsinclude EPO.

In another set of embodiments, the delivery element is implanted in thesubject.

In another set of embodiments, the communication element includes awireless component.

In another set of embodiments, the measuring element includes adisposable component.

In another set of embodiments, the computing element is selected fromlaptop computer, tablet computer, cell phone, table-top computer,networked computing device, and wireless computing device.

The present invention, in yet another aspect, is directed to a methodfor applying an anemia management protocol (AMP) for treating anemia ina human subject, including: measuring a value of at least onebiochemical property related to an anemia status in the subject;determining a difference between the value of the at least onebiochemical property and a predetermined value for the property; and,employing a computing element with a mathematical algorithm to calculatea required dosage for erythropoiesis-stimulating agents based on thedifference. The algorithm may include an integrator or an approximateddiscrete-time integrator, the integrator being described by theequation:

$\frac{z}{z - 1},$

and the approximated discrete-time integrator being described by:

$\frac{z}{z - a},$

wherein the value of a is near 1.

In another aspect, the present invention is directed to a method. In oneset of embodiments, the method includes acts of determining a hemoglobinconcentration in a subject; using a device comprising a controllercomprising an integrator or an approximated discrete-time integrator,and encoding Equations 1-5, to determine a dosage of anerythropoiesis-stimulating agent; and administering the dosage to thesubject.

The present invention, in still another aspect, is directed to a device.In one set of embodiments, the device comprises a receiver fordetermining a hemoglobin concentration in a subject; a controllercomprising an integrator or an approximated discrete-time integrator,and encoding Equations 1-5 to determine a dosage of anerythropoiesis-stimulating agent using the hemoglobin concentration; andan applicator for administrating the dosage to the subject. In anotherset of embodiments, the device comprises a receiver for determining ahemoglobin concentration in a subject; and a controller comprising anintegrator or an approximated discrete-time integrator, and encodingEquations 1-5 to determine a dosage of an erythropoiesis-stimulatingagent using the hemoglobin concentration.

In another aspect, the present invention encompasses methods of makingone or more of the embodiments described herein. In still anotheraspect, the present invention encompasses methods of using one or moreof the embodiments described herein.

Other advantages and novel features of the present invention will becomeapparent from the following detailed description of various non-limitingembodiments of the invention when considered in conjunction with theaccompanying figures. In cases where the present specification and adocument incorporated by reference include conflicting and/orinconsistent disclosure, the present specification shall control. If twoor more documents incorporated by reference include conflicting and/orinconsistent disclosure with respect to each other, then the documenthaving the later effective date shall control.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting embodiments of the present invention will be described byway of example with reference to the accompanying figures, which areschematic and are not intended to be drawn to scale. In the figures,each identical or nearly identical component illustrated is typicallyrepresented by a single numeral. For purposes of clarity, not everycomponent is labeled in every figure, nor is every component of eachembodiment of the invention shown where illustration is not necessary toallow those of ordinary skill in the art to understand the invention. Inthe figures:

FIG. 1 shows simulated Hgb (hemoglobin) responses of a subject (Pat #1)vs. clinical Hgb data;

FIG. 2 shows a block diagram of a discreet feedback control system forone embodiment of the instant invention;

FIG. 3 shows a schematic view of one example of AMP design;

FIG. 4 shows certain EPO dose computation approaches;

FIG. 5 shows resulting Hgb cycling due to incorrect AMP design;

FIG. 6 shows a schematic view of an optimal approach for AMP design inaccordance with certain embodiments of the invention;

FIG. 7 shows a table comparing performance of a prior art protocol and aprotocol based on an embodiment of the instant invention.

FIG. 8 shows clinical results related to the implementation of differentAMPs, including one based on an embodiment of the present invention;

FIG. 9 shows clinical results related to the implementation of differentAMPs, including one based on an embodiment of the present invention;

FIG. 10 shows simulated Hgb (hemoglobin) response of a patient using ananemia management protocol (AMP) design for anerythropoiesis-stimulating agent, OMONTYS;

FIG. 11 shows a method associated with an embodiment of the presentinvention;

FIG. 12 shows a method associated with another embodiment of the presentinvention;

FIG. 13 shows a method associated with another embodiment of the presentinvention; and

FIG. 14 shows a schematic view of a device associated with an embodimentof the instant invention.

DETAILED DESCRIPTION

The present invention is generally directed to methods and devices fordetermining dosing for a medical agent. In some embodiments, amathematical algorithm is employed for computingerythropoiesis-stimulating agents dosing for treating anemia in asubject, e.g., a human subject. Any suitable dosing may be used, e.g.,intravenous, subcutaneous, oral, intraarterial, intramuscular,transdermal, etc. In some cases, dosing for a wide range of subjecttypes and health conditions can be achieved using the devices andmethods disclosed herein.

It should be noted that various embodiments of the invention aregenerally directed to devices and methods able to control theconcentration of hemoglobin in a subject via the administration oferythropoiesis-stimulating agents such as erythropoietin. By using theequations as discussed herein, a device may be able to calculate and insome cases administer a next dose of erythropoiesis-stimulating agentthat is to be applied to the subject in a way such that theconcentration of hemoglobin within the subject remains controlled. Sucha dosing can only be accurately determined using equations as arediscussed herein, although the devices and methods as discussed hereinare generally directed to controlling hemoglobin concentrations withinthe blood of a subject, not to the mathematical equations themselves. Inaddition, control of the concentration of hemoglobin within the blood isof real, concrete, palpable, tangible, and critical use in maintainingthe health of subjects, e.g., having or at risk of anemia; the failureto control such hemoglobin concentrations within the subject couldpotentially lead to adverse medical complications or even death of thesubject. For example, as is described herein, the application of properdoses of an erythropoiesis-stimulating agent, such as erythropoietin, toa subject can often be of critical importance in transforming the healthof the subject, and potentially avoiding adverse medical complicationsor death of the subject.

For example, in one set of embodiments, the present invention isgenerally directed to determining an optimal dosing of anerythropoiesis-stimulating agent (ESA) such as EPO (erythropoietin) orOMONTYS for a subject, for example, an anemic patient. In some cases,the present invention may allow for optimized use of the ESA whileproviding optimal hemoglobin (Hgb) concentration in subjects, e.g., bytreating the subjects using the devices and methods as discussed herein.

Erythropoietin (EPO), secreted primarily by the kidneys (e.g., inresponse to hypoxia), drives the production of red blood cells (RBCs) bystimulating the production of the RBC progenitors within the bonemarrow. In certain conditions, e.g., chronic kidney disease (CKD),endogenously produced EPO is insufficient to maintain normal RBCconcentrations, which may lead to a clinical state of anemia. Oneexample of an erythropoietin that can be applied to a subject isrecombinant human EPO. The discovery of recombinant human EPO (rHuEPO)has shifted the treatment of anemia for subjects on dialysis from bloodtransfusions to rHuEPO therapy. Although more than 20 years have passedsince the discovery of rHuEPO, effectively computing the dose size andfrequency of rHuEPO applications in order to maintain the desired meanconcentration and to minimize variations of Hgb a direct indictor of RBCmass has not been described by others.

Although not wishing to be bound by any theory, the following model isimplemented in various devices and methods in accordance with certainembodiments of the invention. As noted below, certain Anemia ManagementProtocols (AMP) for treating anemia in a subject are implemented byacquiring a sample from the subject, determining a concentration ofhemoglobin in the sample, using the model to determine the next dose ofa suitable erythropoiesis-stimulating agent to be applied to thesubject, and optionally applying the next dose to the subject. In somecases, the model may be implemented, e.g., using an integrator or anapproximated discrete-time integrator to determine certain parameters ofthe model, as those parameters cannot be precisely solved, and can onlybe numerically evaluated using a computer, e.g., via numericalintegration. Thus, a computer or other integration device is typicallyrequired in order to determine the next dose of theerythropoiesis-stimulating agent.

The dynamics of hemoglobin concentration following the administration ofintravenous (IV) EPO or another suitable erythropoiesis-stimulatingagent can be described using a combination of pharmacokinetic (PK) andpharmacodynamics (PD) models, which are outlined as follows. It shouldbe noted that this model is applied in certain embodiments of theinvention, although in some embodiments, other equivalent models may beused to relate hemoglobin to an erythropoiesis-stimulating agent. Forexample, in some embodiments, a model substantially similar to thefollowing, but adding or subtracting one or more correction terms, maybe used, and such modifications may be considered to fall within thescope of the equations outlined as follows.

The PK model outlined as follows comprises a single dynamic pool of EPO,an IV EPO dose as an impulsive input, and a saturable function capturingnonlinear clearance/degradation as shown below. The kinetics of theexogenous EPO, E, is described by the following nonlinear equation:

$\begin{matrix}{{{\frac{d}{dt}{E(t)}} = {{- \frac{V_{\max}E}{{K_{m}^{\prime}V_{d}} + E}} + {d(t)}}},} & (1)\end{matrix}$

where V_(max) denotes maximal clearance/degradation rate of EPO within asubject (e.g., via the kidneys), K_(m)≈K′_(m)V_(d) denotes theconcentration of rHuEPO which produces the half maximal clearance rateof V_(max) in the subject, V_(d) denotes the volume of distribution ofEPO in blood, K′_(m) denotes the concentration of rHuEPO which produceshalf maximal E clearance rate of V_(max) in the subject, and d denotesthe rHuEPO dose as a function of time. rHuEPO is used in this model asan example of an erythropoiesis-stimulating agent, although in otherembodiments of the invention, other erythropoiesis-stimulating agentsmay be used, e.g., in addition or instead of rHuEPO. For example, thismodel can be used for any ESA whose mechanism of action is simulationvia EPOR (EPO) receptor.

This model for subcutaneous administration of EPO includes an additionalterm capturing the absorption process. The total amount of EPO is thesum of exogenous and endogenous levels:

E _(p) =E+E _(en)  (2),

where E_(en) denotes the baseline level of endogenous EPO, E denotes thebaseline level of exogenous EPO, and E_(p) is the total amount of EPOpresent in the subject.

The PD model comprises stimulatory effects of EPO on differentiation,maturation, and proliferation of hematopoietic stem cells intoreticulocytes and maturation into red blood cells. The stimulatoryeffect of the blood EPO level on the production of new reticulocytes isdescribed by a nonlinear, time-delayed function (indicated by the termT_(D)):

$\begin{matrix}{{{k_{in}\left( {t - T_{D}} \right)} = \frac{S_{\max}{E_{P}(t)}}{{{SC}_{50}^{\prime}V_{d}} + {E_{P}(t)}}},} & (3)\end{matrix}$

where k_(in) is the production rate of new reticulocytes in the subject(offset by a time-delay T_(D)), S_(max) is the maximal stimulation rateof new reticulocytes, SC₅₀≈SC′₅₀′V_(d) denotes the concentration of EPOwhich produces a half maximal production rate of new reticulocytes inthe subject (SC′₅₀ denotes the concentration of EPO which produces halfmaximal production rate and V_(d) denotes the volume of distribution ofEPO in blood), and T_(D) (or t_(D)) is the time required for pluripotenthematopoietic stem cells to become RBCs (i.e., the progression of thestem cells through burst-forming units, colony-forming units,erythroblasts, and reticulocytes). It should be noted that theseequations are nonlinear and therefore cannot be explicitly solved, butinstead can only be evaluated numerically. In addition, many of theconstants described above can be estimated using many availableidentification algorithms based on clinical EPO and Hgb time series.

The RBC pool dynamics is described by the following differentialequation:

$\begin{matrix}{{{\frac{d}{dt}{{RBC}(t)}} = {{k_{in}\left( {t - t_{D}} \right)} - {\int_{0}^{\infty}{{k_{in}\left( {t - t_{D} - \lambda} \right)}{_{RBC}\left( {{t - \lambda},\lambda} \right)}\ d\; \lambda}}}},} & (4)\end{matrix}$

where RBC(t) is the mass of red blood cells (which the reticulocytesmature into),

_(RBC)(l,t) is the probability density function of the lifespan t of anRBC entering the pool at time

(in the above integral,

=t−λ and t=λ), and t_(D)=T_(D) is the time required for pluripotenthematopoietic stem cells to become RBCs. In addition, k_(in) is theproduction rate of new reticulocytes in the subject (offset by atime-delay t_(D)), as described in Equation 4. As is discussed herein,this equation may be evaluated in some embodiments using an integratoror an approximated discrete-time integrator.

Finally, the concentration of hemoglobin is assumed fixed with respectto the concentration of red blood cells in the subject:

Hgb=K _(Hgb)RBC  (5),

where RBC is the mass of red blood cells, and K_(Hgb) is the averagehemoglobin concentration per RBC, also known as the mean corpuscularhemoglobin (MCH).

Accordingly, based on the above equations, starting with a known dose oferythropoietin or another suitable erythropoiesis-stimulating agent(e.g., such as OMONTYS), and adding in known or determinable constantssuch as V_(max) and K′_(m), the concentration of hemoglobin in a subjectmay be determined. Conversely, if a specific hemoglobin amount orconcentration is desired in a subject, the above equations may be usedto determine the next dose of a erythropoiesis-stimulating agent to giveto the subject.

In one set of embodiments, a device comprising a controller is used topredict a hemoglobin concentration or amount in a subject based on adose of an erythropoiesis-stimulating agent given to the subject. Forexample, the prediction may be made for a future moment in time, or usedto determine the success or failure of a concurrently occurringtreatment. In another set of embodiments, a device comprising acontroller is used to determine a suitable dose of anerythropoiesis-stimulating agent to be given to a subject based on adesired hemoglobin concentration or amount.

These calculations may be performed by a device comprising a controllerwith appropriate hardware and/or software, e.g., for numericallyevaluating the above equations, e.g., as discussed herein. It should benoted that these equations, in total, require mathematical operationssuch as numerical integration of probability density functions, whichcannot be precisely solved, but can only be numerically evaluated usinga computer, e.g., using computational discrete-time integrator methodssuch as the Forward Euler, Backward Euler, Trapezoidal method,second-order accurate methods, or third order accurate methods.Accordingly, it is generally not possible for a human to evaluate theseequations with a sufficient degree of accuracy, and thus, a devicecomprising a controller such as is described herein is used tonumerically evaluate the above equations, in various embodiments.

Accordingly, in one aspect, the present invention is generally directedto devices and methods for treating a subject with serial doses of anerythropoiesis-stimulating agent (ESA). In one set of embodiments, theconcentration of hemoglobin in a subject is determined, directly orindirectly, and by using techniques such as those described herein, thenext dose of the erythropoiesis-stimulating agent to be given to thesubject is then computed or calculated.

One non-limiting example of an ESA is erythropoietin. Erythropoietin ismade endogenously by a subject, and can also be obtained commercially(e.g., as recombinant human erythropoietin); in some cases, the subjectmay receive erythropoietin from both sources, which need to be balancedagainst each other as is discussed herein. For example, erythropoietinmay be produced by recombinant DNA technology in mammalian cell culture.Recombinant EPO has a variety of glycosylation patterns giving rise toalpha, beta, delta, and omega forms, for example Epogen, Procrit, andAnserp, made by Amgen. In one embodiment, the erythropoietin given tothe subject is recombinant human erythropoietin (rHuEPO).

Another example of an ESA is OMONTYS (peginesatide). OMONTYS is asynthetic, pegylated, peptide-based ESA that mimics the structure oferythropoietin. Yet other non-limiting examples of ESAs arehypoxia-inducible factors (HIFs), transcription factors that respond todecreases in oxygen, or hypoxia, in the cellular environment. Severalcompanies, for example Akebia Therapeutics and Fibrogen, are currentlyinvolved in clinical trials that study the therapeutic potential ofthese inhibitors in treating patients with anemia of chronic disease.

The subject may be one in which it is desired to control or normalizehemoglobin concentrations. The subject may be human or non-human, e.g.,a non-human mammal. The subject may be anemic, for example, due tochronic kidney disease (e.g., where the subject may or may not be ondialysis), chemotherapy, or the effects of zidovudine (AZT) and othermedications used to treat HIV infection (which often cause anemia as aside effect).

One set of embodiments is generally directed to a device for deliveringerythropoiesis-stimulating agents to a subject. Typically, a sample(e.g., of blood) from the subject is acquired and analyzed (e.g., asdiscussed herein) to determine the concentration of hemoglobin in thesample. Other biochemical properties may also be determined, in additionor instead of hemoglobin in the sample, for example, complete bloodcount, soluble EPO receptors (sEPOR), iron test, and Ferritin, which maybe used to estimate hemoglobin concentrations using routine techniquesknown to those of ordinary skill in the art. These properties may bedetermined, and in some cases, used to estimate the concentration ofhemoglobin, e.g., for use in the equations described herein. Typically,serial samples are taken from the subject. For example, the samples maybe taken daily, weekly, biweekly, every 4 weeks, monthly, etc. In somecases, however, the samples are taken more frequently, e.g., hourly orevery few hours.

FIG. 1 shows the applicability of Equations 1-5 to predict Hgb responseof a chronic kidney disease subject (“Pat #1”) to EPO administration, asan illustrative non-limiting example. Specifically, FIG. 1 shows twopredicted Hgb responses of the subject based on Equations 1-5 vs. theclinical data (top), and the administered EPO doses (bottom). It isobserved that the first set of estimated parameters (id#1) successfullypredicted the clinical Hgb response up to day 325 (approximately), butfailed to do so thereafter. This required a second set of parameters(id#2) to be estimated for the remaining period from day 325 to day 473.Most subjects undergo changes in erythropoiesis over time resulting in atime-varying model using Equations 1-5. Such commonplace changes renderprotocols based on open-loop models inefficient. In other words, withoutthe presence of a controller (as discussed below) to discretize andimplement an integrator or an approximated discrete-time integrator,Equations 1-5 as discussed above may not adequately be used to predicthemoglobin concentrations in the subject, or future doses of a suitableerythropoiesis-stimulating agent to be applied to the subject, as isdiscussed herein. It should also be noted that, as discussed herein,some of the controllers discussed herein are robust and able to respondto disturbances in the subject, e.g., bleeding, cancer, bacterialinfections, blood transfusions, etc. that Equations 1-5 are otherwiseunable to incorporate.

Accordingly, in one set of embodiments, a device comprising a controlleris used to regulate the concentration or amount of hemoglobin (Hgb) in asubject. The controller may accept input based on a dosage of an ESAgiven to a subject, and be used to determine the concentration or amountof hemoglobin, or the controller may accept input based on a desiredconcentration or amount of hemoglobin (Hgb), and be used to determine asuitable dosage of an erythropoiesis-stimulating agent that wouldproduce such as a result. In some embodiments, other biochemicalproperties may also be determined, in addition or instead of hemoglobin,as discussed herein, and such properties used instead of or in additionto the desired concentration or amount of hemoglobin, e.g., in theequations discussed above.

One objective, in certain embodiments of the invention, of an anemiamanagement protocol (AMP), i.e., a controller (in the terminology ofcontrol engineering), is to regulate hemoglobin (Hgb) concentrations toremain within a desired range, minimization of over- and/or under-shoot,and/or to moderate changes in response due to disturbances in thesubject. Examples of such disturbances that may be taken into account inthe controller include, bleeding, cancer, bacterial infections, bloodtransfusions, or the like, that may alter the availability of hemoglobinin the subject and/or the amount of oxygen delivery that is availabledue to changes in hemoglobin concentrations, either positively ornegatively (in contrast, prior art protocols, e.g., using dose-responsepredictions, are typically incapable of accounting for suchdisturbances). In robust control methods, a single controller isdesigned based on a nominal model, a quantitatively defined modeluncertainty, and the desired performance. In this context, an estimatedmodel can be considered a nominal model, at least in certain embodimentsof the invention. One then may group subjects into several groups, forexample based on the amount of EPO required to achieve the desired Hgbconcentration. Within each such group, one defines a range for eachparameter that includes all likely values for subjects in that group.This defines a model uncertainty. Desired performance parameters caninclude, for example, minimal overshooting of Hgb response, reducedcycling, and maintenance of Hgb within a specified range.

There are several options available for the design of the controller.One approach is to discretize the model based on the dosing protocol,weekly as an example. A block diagram of the discrete-time system isshown in FIG. 2 as an illustrative non-limiting example. It includes thefollowing components: a protocol (e.g., a discrete-time controllerprotocol) C(z) operating once per dose decision period (T), whose inputsignal is the difference between target Hgb and actual Hgb and output isthe dose of an ESA, and the discrete-time plant P(z) representing thedynamics between administered ESA doses and resulting Hgb (for example,the continuous-time plant may be described herein by Equations 1-5, asnoted above).

Thus, in one embodiment of the present invention, a controller maycomprise a discrete-time controller protocol (C(z)) and a plant P(z). Itshould be noted, however, that the present invention is not limited onlyto the controller as is shown in FIG. 2. In other embodiments of theinvention, other blocks may be present, and/or the blocks may bearranged in a different order.

As a non-limiting example, as is shown in FIG. 2, the difference betweenthe target and actual concentrations of hemoglobin is applied to adiscrete-time controller protocol (C(z)) to determine a suitable levelof an ESA (such as rHuEPO as is shown in FIG. 2) that is to be appliedto a subject, then that level of the ESA is applied to the plant model(P(z)) (e.g., as is implemented using Equations 1-5 to determine theconcentration of hemoglobin (Hgb) that will be present in the subject atthe next period of time T.

Non-limiting examples of controller protocols (C(z)) are discussedbelow. However, in general, the discrete-time controller protocol mayproceed by using the current input signal (for example, hemoglobinconcentration), and the previous input and output signals to determinethe next output signal (e.g., the amount of anerythropoiesis-stimulating agent that is required). A variety ofdifferent controller protocols may be used, as is discussed herein. Forexample, in some embodiments, an estimation of the responsiveness in asubject between the amount of erythropoiesis-stimulating agent that isadministered to the subject and the resulting hemoglobin concentrationmay be used within the controller. This relationship may be termed thegain. Thus, in one set of embodiments, the controller may comprise adiscrete-time controller protocol that uses the gain as the input. Thegain may be set to a fixed constant, e.g., based on the subject's use ofan erythropoiesis-stimulating agent, or the gain may be estimated usingmeasurements or samples taken from a subject, e.g., at different pointsin time.

The computations required by the controller (e.g., to implement ananemia management protocol) may be performed using a device having theseequations encoded in hardware and/or software. At that later point intime, in some embodiments of the invention, the device may alsoadminister that dosage, e.g., intravenously, subcutaneously, orally,etc. For example, the device may be wristwatch or other portable devicethat is able to receive a sample of blood, calculate the next dose usinga controller, as discussed herein, and apply the next dose to thesubject at the appropriate time. The device, in certain embodiments, mayinclude a hemoglobin sensor that can determine the hemoglobinconcentration from the sample of blood, e.g., using pulse oximetery(reflectance or transmissive) sensors, spectrophotometric sensors,electrochemical sensors, or the like. Many such hemoglobin sensors maybe readily obtained commercially. In addition, in one set ofembodiments, the device may further comprise a needle and a reservoirfor containing a suitable erythropoiesis-stimulating agent. Thus, forexample, upon receiving a determination of the concentration ofhemoglobin in a subject, the controller may determine an appropriatedosage of a suitable erythropoiesis-stimulating agent, and the devicemay then deliver that dosage of the erythropoiesis-stimulating agentfrom the reservoir via the needle.

As mentioned, the device may also include a receiver for determining thehemoglobin concentration in a subject. For instance, the receiver mayinclude a hemoglobin sensor for determining hemoglobin in a sample ofblood withdrawn from the subject (e.g., as discussed herein), or thereceiver may include an input device for entering a concentration ofhemoglobin (for example, if an external device was used to determine theconcentration of hemoglobin in a sample of blood withdrawn from thesubject. As various examples, the input device may include a keyboard(e.g., for manual entry of the hemoglobin concentration), or a USB port,a transceiver, etc. that allows the input device to receive input from acomputer or other external device.

The biochemical property most usually measured is the concentration ofhemoglobin, although other properties could also be used in otherembodiments. Deviations from target hemoglobin concentration allow fordetermination of appropriate ESA dosing for a subject. In someembodiments, the algorithm allows for predetermined target performancein spite of potential disturbances—such as bleeding, cancer, bacterialinfection, blood transfusions, or the like—that may lead to changes inthe amount of blood and/or changes in the amount of oxygen delivery toorgans within the subject, e.g., due to changes in hemoglobinconcentrations. Other potential disturbances include, but are notlimited to, levels of B12 and folate, iron availability, inflammation,uremic toxins, hypothyroidism, hypersplenism, ongoing infection, etc.

Most clinicians rely on an expert system comprising a set of rules basedon past experience and retrospective studies. From the clinician'sviewpoint, this approach is practical; it relies on a few,readily-available measurements, and is applicable to the entirepopulation. Indeed, a necessary factor in designing a therapeuticprotocol is to understand the biological dynamics.Pharmacokinetic/pharmacodynamics (PK/PD) studies help to predict Hgbresponse to rHuEPO dosing, and to develop open-loop models of thiscausal relationship. However, as is discussed herein, when dosing of anerythropoiesis-stimulating agent (ESA) such as rHUEPO is based on Hgbconcentrations, the response is that of a closed-loop system. In otherwords, the relationship between the ESA and the resulting Hgbconcentration cannot be inferred from the open-loop PK/PD studies thatare commonly used by others. In contrast, as is discussed herein,various embodiments are used to predict Hgb concentrations in a subject,by analyzing the closed-loop system formally (e.g., with a controller),explicitly taking into account the periodicity of the protocols and theuncertain parameters of the PK/PD models.

Typical anemia management protocols are designed from a viewpoint wherethe designer (i.e., doctor) is too close to the treatment: the designerobtains an Hgb measurement, then makes an EPO dose decision. Forinstance, once a new Hgb measurement is obtained, the designerdetermines the next dose of ESA based on the expected dose-responsebehavior, e.g., based on how the designer predicts that the subject willrespond to this dose as illustrated in FIG. 4. This is common tovirtually all drug dosing protocols. However, in this approach, thedesigner cannot “see” the overall feedback system for the cause-effectrelationship of EPO-to-Hgb (e.g., as implemented by a controller as isdiscussed in various embodiments herein). Thus, the designer in suchprior art systems can only observe a ‘local’ viewpoint, and has no wayof accounting for other effects, such as the relationship between theESA and the resulting Hgb concentration, especially with respect totime. However, when drug dosing is done on a repetitive nature, theresulting Hgb dynamics are often different from the ‘designer’sdose-response understanding, no matter how accurate this understandingis, and thus, the resulting predictions will be lead astray (see FIG. 5and resulting Hgb cycling due to incorrect design). However, thisproblem has not previously been recognized, and many designers ordoctors continue to make predictions based only on expected (or guessed)dose-response behavior, and do not take into account the relationshipbetween the previous dose of the ESA and the resulting Hgbconcentration.

Accordingly, in some embodiments, the present invention is generallydirected to a “large view” of dynamic feedback interaction, e.g., toaccount for this relationship, as schematically suggested in FIG. 6. Theinvention, in some embodiments, recognizes that a new system is createdthrough feedback, and by taking into account the relationship theprevious dose of the ESA and the resulting Hgb concentration, e.g., viaa controller, more optimal dosing of an ESA may be achieved in asubject. To illustrate this, the systems and methods described in thefollowing non-limiting examples are designed based on short andlong-term performance objectives such as avoiding overshooting andgaining stability. Performance tradeoffs are evaluated a priori as afunction of modeling fidelity.

Attention is now turned to FIG. 11 which shows a non-limiting embodimentof the present invention, describing a method for computingerythropoiesis-stimulating agents (ESAs) dosing (e.g., intravenously,subcutaneously, orally, etc.), for treating anemia in a subject, such asa human subject, including the following steps: measuring a value of atleast one biochemical property related to an anemia status in thesubject; determining a difference between the value of the at least onebiochemical property and a predetermined optimal value for the property;and, employing a computing element with a mathematical algorithm tocalculate a required ESA dosage based on the difference, wherein thealgorithm maintains predetermined target performance criteria for arange of biochemical property values in a plurality of predeterminedphysiological factors affecting the value of the at least onebiochemical property.

A plurality of predetermined physiological factors may be used,including the lifespan of red blood cells in the range of 20-200 days,mean corpuscular hemoglobin (MCH) in the range of 25-42 picograms/cell,and the time from ESA stimulation to release of new red blood cell intocirculation in the range of 3-9 days. The biochemical property mostusually measured is the concentration of hemoglobin, although otherproperties could also be used in other embodiments. Deviations fromideality for hemoglobin concentration allow for determination ofappropriate ESA dosing for a subject. In this embodiment, the algorithmhas a fixed value for a range of hemoglobin concentration values,generally but not necessarily, 8 to 14 g/dl of blood.

Attention is now turned to FIG. 12, where is described anothernon-limiting embodiment of a method for applying an Anemia ManagementProtocol (AMP) for treating anemia in a subject, such as a humansubject, including: measuring a value of at least one biochemicalproperty related to an anemia status in the subject; determining adifference between the value of the at least one biochemical propertyand a predetermined value for the property; and, employing a computingelement with a mathematical algorithm to calculate a required dosage forerythropoiesis-stimulating agents (ESAs) based on the difference,wherein the algorithm includes a step for reducing the sensitivity ofthe AMP to the variability in the subject's responsiveness to the ESAs.

Attention is now turned to FIG. 13 which describes yet anothernon-limiting embodiment of a method for applying an Anemia ManagementProtocol (AMP) for treating anemia in a human subject, including:measuring a value of at least one biochemical property related to ananemia status in the subject; determining a difference between the valueof the at least one biochemical property and a predetermined value forthe property; and, employing a computing element with a mathematicalalgorithm to calculate a required dosage for erythropoiesis-stimulatingagents (ESAs) based on the difference.

In some cases, the algorithm may include an integrator or anapproximated discrete-time integrator, the integrator being described bythe equation:

$\frac{z}{z - 1},$

and the approximated discrete-time integrator being described by:

$\frac{z}{z - a},$

wherein the value of a is selected to be near 1. The variable z isdefined so that z⁻¹ denotes a unit sample time delay. That is, at thesample time kT the integrator output y(kT) is related to the currentinput signal u(kT) by the difference equation:

y(kT)=u(kT)+y(kT−T),

where y(kT−T) is the output signal in the previous sample time.Accordingly, if the integrator output is the concentration of a suitableerythropoiesis-stimulating agent and the input signal is hemoglobinconcentration, then the above equation may be used to capture theirrelationship.

Attention is now turned to FIG. 14 which shows a schematic view ofnon-limiting example device 1300 for delivering an optimized amount ofan erythropoiesis-stimulating agents (ESAs) (e.g., intravenously,subcutaneously, orally, etc.), for treating anemia in a human subject1303, including: a measuring element 1305 adapted to measure a value ofat least one biochemical property related to an anemia status in thesubject; a communication element 1310 adapted to communicate the valueto a computing element 1320 adapted to calculate a difference betweenthe value of said at least one biochemical property and a predeterminedvalue or range of values for the property, the element adapted to employa mathematical algorithm to calculate a required ESA dosage based on thedifference, wherein the algorithm remains fixed for a predeterminedrange of target values of the property; and, optionally, a deliveryelement 1330 for delivering said ESA to the subject 1303. For example,delivery element 1330 may include a needle, such as a hypodermic needle,and a reservoir containing the ESA.

In most applications, the erythropoiesis-stimulating agent will be EPO,although other erythropoiesis-stimulating agents that could also be used(in addition to or instead of EPO) have been previously discussedherein. In some embodiments, the delivery element 1330 may be implanteddirectly into subject 1303. In some embodiments, the communicationelement 1310 includes wireless component for moving data betweencomponents of the device 1300. Any component of the device 1300 thatcomes into direct contact with subject 1300 or bodily fluids of subject1303 may be disposable in certain cases. As non-limiting example, thecomputing element may be a laptop computer, a tablet computer, a cellphone, a table-top computer, a networked computing device, a wirelesscomputing device, or the like.

As used herein the term “about” refers to +/−10%. As used herein, thesingular form “a”, “an” and “the” include plural references unless thecontext clearly dictates otherwise. For example, the term “a compound”or “at least one compound” may include a plurality of compounds,including mixtures thereof.

The following examples are intended to illustrate certain embodiments ofthe present invention, but do not exemplify the full scope of theinvention.

Example 1

In this example, comparisons were made between a traditional EPO(erythropoietin) dosing protocol and a protocol based on an embodimentof the instant invention. The model as described in Equations 1-5 abovewas used in a simulation, with parameters estimated based on aretrospective data corresponding to 49 subjects collected over a periodof 18 months. The typical protocol used in this example was a “one-sizefits all” protocol, e.g., population-oriented and having a set of rulesbased on Hgb trending and Hgb ranges. Both protocols assumed weekly EPOdose adjustments with 3×/week administration. Protocol performancecriteria were as follows:

-   -   Achieve Hgb_(SS)=11.25 g/dL at steady state.    -   Reduce overshooting    -   Robustness, i.e., to be effective for the entire set of models        within that group.

Subjects were generally categorized based on their weekly use of EPO:hyper-responsive (<12000 IU/week), intermediate-responsive (between12000 and 30000 IU/week), and hypo-responsive (>30000 IU/week). Anotherpossible categorization was based on the steady-state gain of thesubject's gain:

gain=0.295(μ_(RBC)) k _(in)(d _(SS)),

where μ_(RBC) is the mean RBC lifespan in the subject (typically 20-200days), d_(SS) denotes the constant EPO dose required to yield aspecified steady-state Hgb concentration Hgb_(SS) in the subject, and k_(in)(d_(SS)) denotes the mean production rate of new reticulocytes. k_(in) is discussed above in Equation 3. d_(ss) may be computed usingnumerical simulations to compute the value of d_(ss) that results in thedesired target Hb. See also Nichols, et al., “Simplification of anerythropoiesis model for design of anemia management protocols in endstage renal disease,” Conf. Proc. IEEE Eng. Med. Biol. Soc., 2011:83-86,2011, incorporated herein by reference in its entirety.

The subjects were categorized into four groups: hypo-responsive(gain<8e⁻⁴), intermediate-responsive (8e⁻⁴≤gain<18e⁻⁴), hyper-responsive(18e⁻⁴≤gain<30.42e⁻⁴), and very hyper-responsive (gain≥30.42e⁻¹).(8e⁻⁴˜0.145, 18e⁻⁴˜0.330, and 30.42e⁻⁴˜0.557.) The following controllerswere individualized for each group:

${C(z)} = \left\{ \begin{matrix}{\frac{908.7\left( {z - 0.795} \right)}{z - 1}\mspace{14mu}} & {{hypo}\mspace{14mu} {responsive}} \\{\frac{297.6\left( {z - 0.795} \right)}{z - 1}\mspace{14mu}} & {{intermediate}\mspace{14mu} {responsive}} \\{\frac{140.2\left( {z - 0.795} \right)}{z - 1}\mspace{14mu}} & {{hyper}\mspace{14mu} {responsive}} \\{\frac{74.1\left( {z - 0.795} \right)}{z - 1}\mspace{14mu}} & {{very}\mspace{14mu} {hyper}\mspace{14mu} {responsive}}\end{matrix} \right.$

The variable z is defined so that z⁻¹ denotes a unit sample time delay.That is, at the sample time kT the controller's output y(kT) is relatedto the current input signal u(kT) (dose of the ESA, e.g., EPO) by thedifference equation (shown here for the hypo responsive controller):

y(kT)=908.7(u(kT)−0.795u(kT−T))+y(kT−T)

where y(kT−T) is the output signal in the previous sample time. See alsoNichols, et al., “Simplification of an erythropoiesis model for designof anemia management protocols in end stage renal disease,” Conf. Proc.IEEE Eng. Med. Biol. Soc., 2011:83-86, 2011, incorporated herein byreference in its entirety, for a discussion of responsiveness insubjects.

To study protocol performance under intrasubject variability, randomvariations were introduced in the response to EPO stimulation (0 mean,0.05 SD). The performance requirements for the new protocol were allmet: the target of Hgb of 11.25 g/dL was within the desired range androbustness. Performance comparisons between the new protocol and thetraditional treatment demonstrated that in each of the groups, the newanemia management protocol outperformed the traditional anemiamanagement protocol as shown in FIG. 7, where “New” refers to anembodiment of the instant invention and “Current” refers to atraditional protocol as generally applied. In particular, larger Hgbvariability was observed with the traditional protocol. Finally, meanweekly EPO use with the traditional protocol was at least 10% greater(5.5% in very hyper-responsive) than that with the new protocol.

Example 2

FIG. 8 shows clinical results related to the implementation of differentanemia management protocols (AMPs) including one based on an embodimentof the present invention. Up to around day 670, EPO (erythropoietin)doses for a subject (#10) have been computed using several anemiamanagement protocols. During this time period, undesirable Hgb(hemoglobin) cycling and a lack of Hgb remaining in a range wereobserved.

In contrast, a new anemia management protocol (implemented using oneembodiment of the present invention) was switched on at day 670. It wasfound that the new protocol was able to smoothly guide the subject's Hgbto its target and maintain it within the target range. In allperformance measures (data not shown), the new anemia managementprotocols outperformed the control anemia management protocols.

Example 3

In this example, to demonstrate that in order to improve the AMPs(anemia management protocols) performance as the dynamics of subjectsvary with time, the gain of AMP may be adjusted whenever a change in thesubject's responsiveness (the “gain”) is detected. This change wasstudied in this example in one of two ways:

1. The subject moved from one responsiveness group to another, in whichcase, the controller may be updated according to the particularcontrollers for that group, or

2. The gain of the subject's controller is modified in proportion to thegain, for example, if the gain has increased by 20%, then thecontroller's gain is decreased by 20%.

This individualization of the protocol as related to various embodimentsof the present invention requires the estimation of a subject'sresponsiveness (i.e., the gain). There are several approaches that maybe used for estimating this value, for example, least square estimationor the Kalman filter or one of its extensions. FIG. 9 illustrates such acase in a clinical study. Similar to the results in Example 2, up toaround day 670, EPO (erythropoietin) doses for the subject have beencomputed using several AMPs. During this time period, undesirable Hgb(hemoglobin) cycling and a lack of Hgb remaining in a desired range wereobserved.

A new AMP (implemented using one embodiment of the present invention)was switched on at day 670. The new AMP was able to smoothly guide thesubject's Hgb to its target. However, starting around day 800, thesubject developed a slow internal bleeding that was completely overcomeonly two months later. The new protocol detected a corresponding changein the subject's responsiveness and adapted the AMP accordingly. Theadaptation was successful and that the AMP overcame the bleeding andsuccessfully guided Hgb to its target without cycling. In spite of thislengthy episode of bleeding, the new AMP (including adaptation to thesubject's changing condition) outperformed traditional AMPs in terms ofperformance measures.

Example 4

This example demonstrates the applicability of an anemia managementprotocol (AMP) designed for the recently FDA-approved ESA OMONTYS madeby Affimax. The basic pharmacokinetic/pharmacodynamics model estimatedin Example 1 (see FIG. 1) was used in this example, and PK parameterswere modified to reflect the mean drug half-life of 48 hours. Thereported conversion of Epogen dose to OMONTYS dose was also used. Thesubject's endogenous Hgb was set to 8.5 g/d, and fluid variability wasmodeled using a multiplicative white noise of mean 1 and standarddeviation of 0.023. The ability of the new AMP to guide the subject toits Hgb target of 11.25 g/l and stabilize it around that concentrationwith minimal cycling is demonstrated in FIG. 10.

Throughout this application, various embodiments of this invention maybe presented in a range format. It should be understood that thedescription in range format is merely for convenience and brevity andshould not be construed as an inflexible limitation on the scope of theinvention. Accordingly, the description of a range should be consideredto have specifically disclosed all the possible subranges as well asindividual numerical values within that range. For example, descriptionof a range such as from 1 to 6 should be considered to have specificallydisclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numberswithin that range, for example, 1, 2, 3, 4, 5, and 6. This appliesregardless of the breadth of the range.

Whenever a numerical range is indicated herein, it is meant to includeany cited numeral (fractional or integral) within the indicated range.The phrases “ranging/ranges between” a first indicate number and asecond indicate number and “ranging/ranges from” a first indicate number“to” a second indicate number are used herein interchangeably and aremeant to include the first and second indicated numbers and all thefractional and integral numerals there between.

While several embodiments of the present invention have been describedand illustrated herein, those of ordinary skill in the art will readilyenvision a variety of other means and/or structures for performing thefunctions and/or obtaining the results and/or one or more of theadvantages described herein, and each of such variations and/ormodifications is deemed to be within the scope of the present invention.More generally, those skilled in the art will readily appreciate thatall parameters, dimensions, materials, and configurations describedherein are meant to be exemplary and that the actual parameters,dimensions, materials, and/or configurations will depend upon thespecific application or applications for which the teachings of thepresent invention is/are used. Those skilled in the art will recognize,or be able to ascertain using no more than routine experimentation, manyequivalents to the specific embodiments of the invention describedherein. It is, therefore, to be understood that the foregoingembodiments are presented by way of example only and that, within thescope of the appended claims and equivalents thereto, the invention maybe practiced otherwise than as specifically described and claimed. Thepresent invention is directed to each individual feature, system,article, material, kit, and/or method described herein. In addition, anycombination of two or more such features, systems, articles, materials,kits, and/or methods, if such features, systems, articles, materials,kits, and/or methods are not mutually inconsistent, is included withinthe scope of the present invention.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of.” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

It should also be understood that, unless clearly indicated to thecontrary, in any methods claimed herein that include more than one stepor act, the order of the steps or acts of the method is not necessarilylimited to the order in which the steps or acts of the method arerecited.

In the claims, as well as in the specification above, all transitionalphrases such as “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of and” consistingessentially of shall be closed or semi-closed transitional phrases,respectively, as set forth in the United States Patent Office Manual ofPatent Examining Procedures, Section 2111.03.

What is claimed is: 1-46. (canceled)
 47. A method for treating anemia ina subject, comprising: (a) determining a concentration of at least onebiochemical property in the subject; (b) using a feedback controller tocalculate a dosage of an erythropoiesis-stimulating agent based on theconcentration of the at least one biochemical property, wherein thecontroller comprises an algorithm including an integrator or anapproximated discrete-time integrator; (c) administering the dosage ofthe erythropoiesis-stimulating agent to the subject; and (d) repeatingsteps (a) through (c) a plurality times.
 48. The method of claim 47,wherein the subject is human.
 49. The method of claim 47, wherein thesubject has renal failure.
 50. The method of claim 47, wherein saidbiochemical property is hemoglobin concentration.
 51. The method ofclaim 47, wherein said biochemical property is iron concentration. 52.The method of claim 47, wherein the erythropoiesis-stimulating agentcomprises erythropoietin (EPO) and/or recombinant human erythropoietin(rHuEPO) and/or novel erythropoiesis stimulating protein (NESP) and/orHIF stabilizing agent.
 53. The method of claim 47, wherein saidintegrator is described by the equation $\frac{z}{z - 1},$ and saidapproximated discrete-time integrator is described by $\frac{z}{z - a},$wherein the value of a is near
 1. 54. The method of claim 53, whereinsaid discrete-time integrator is selected from the following: ForwardEuler, Backward Euler, Trapezoidal method, second-order accurate method,or third order accurate method.
 55. The method of claim 47, wherein thefeedback controller encodes Equations 1-5.
 56. A device for treatinganemia in a subject, comprising: a receiver for determining aconcentration of at least one biochemical property in the subject; afeedback controller configured and arranged to calculate a dosage of anerythropoiesis-stimulating agent based on the concentration of the atleast one biochemical property, wherein the controller comprises analgorithm including an integrator or an approximated discrete-timeintegrator; and an applicator for administering the dosage of theerythropoiesis-stimulating agent to the subject.
 57. The device of claim56, wherein the device further comprises a needle for withdrawing bloodfrom the subject.
 58. The device of claim 56, wherein the device furthercomprises a reservoir containing the erythropoiesis-stimulating agent.59. The device of claim 56, wherein the receiver further comprises ahemoglobin sensor.
 60. The device of claim 56, wherein the receiverfurther comprises an iron sensor.
 61. The device of claim 56, whereinthe erythropoiesis-stimulating agent comprises erythropoietin (EPO). 62.The device of claim 56, wherein the erythropoiesis-stimulating agentcomprises novel erythropoiesis stimulating protein (NESP).
 63. Thedevice of claim 56, wherein the erythropoiesis-stimulating agentcomprises HIF stabilizing agent.
 64. The device of claim 56, whereinsaid integrator is described by the equation $\frac{z}{z - 1},$ and saidapproximated discrete-time integrator is described by $\frac{z}{z - a},$wherein the value of a is near
 1. 65. The device of claim 64, whereinsaid discrete-time integrator is selected from the following: ForwardEuler, Backward Euler, Trapezoidal device, second-order accurate device,or third order accurate device.
 66. The device of claim 56, wherein thefeedback controller encodes Equations 1-5.